Topic
Toeplitz algebra
About: Toeplitz algebra is a research topic. Over the lifetime, 234 publications have been published within this topic receiving 3739 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the invariant subspace structure of a class of semigroup algebras, called hyper-reflexive, is described algebraically by S∗ i Sj = δijI for 1 ≤ i, j ≤ n; (F)
Abstract: In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a non-commutative analytic Toeplitz algebra on n variables. The case we make for this analogy is very compelling. In particular, in this paper, the key to the invariant subspace analysis is a good analogue of the Beurling theorem for invariant subspaces of the unilateral shift. This leads to a notion of inner–outer factorization in these algebras. In a sequel to this paper [13], we add to this evidence by showing that there is a natural homomorphism of the automorphism group onto the group of conformal automorphisms of the ball in Cn. A free semigroup algebra is the weak operator topology closed algebra generated by a set S1, . . . , Sn of isometries with pairwise orthogonal ranges. These conditions are described algebraically by S∗ i Sj = δijI for 1 ≤ i, j ≤ n; (F)
282 citations
TL;DR: In this paper, the authors consider the quasi-lattice ordered groups (G, P ) introduced by Nica and realize their universal Toeplitz algebra as a crossed product B P ⋊ P by a semigroup of endomorphisms.
233 citations
TL;DR: The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators as discussed by the authors.
Abstract: The non-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup onn generators. We obtain a distance formula to an arbitrary WOT-closed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is used to obtain Nevanlinna-Pick type interpolation theorems
208 citations
TL;DR: In this article, the Toeplitz-Cuntz-Krieger algebras of directed graphs were analyzed and the uniqueness theorem for O(n) was proved.
Abstract: Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz algebras O_n, and the Cuntz-Krieger algebras O_B. Here we analyse the representations of the corresponding Toeplitz algebra. One consequence is a uniqueness theorem for the Toeplitz-Cuntz-Krieger algebras of directed graphs, which includes Cuntz's uniqueness theorem for O_\infty.
201 citations
Posted Content•
TL;DR: In this paper, the results of interpolation by elements in the noncommutative analytic Toeplitz algebra $F^\infty$ (resp. Nevanlinna-Pick) with consequences to the interpolation of bounded operator-valued analytic functions in the unit ball of ${\bf C}^n$ are obtained.
Abstract: General results of interpolation (eg. Nevanlinna-Pick) by elements in the noncommutative analytic Toeplitz algebra $F^\infty$ (resp. noncommutative disc algebra $A_n$) with consequences to the interpolation by bounded operator-valued analytic functions in the unit ball of ${\bf C}^n$ are obtained.
Non-commutative Poisson transforms are used to provide new von Neumann type inequalities. Completely isometric representations of the quotient algebra $F^\infty/J$ on Hilbert spaces, where $J$ is any $w^*$-closed, 2-sided ideal of $F^\infty$, are obtained and used to construct a $w^*$-continuous, $F^\infty/J$--functional calculus associated to row contractions $T=[T_1,\dots, T_n]$ when $f(T_1,\dots,T_n)=0$ for any $f\in J$. Other properties of the dual algebra $F^\infty/J$ are considered.
131 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 11 |
| 2020 | 13 |
| 2019 | 19 |
| 2018 | 17 |
| 2017 | 14 |
| 2016 | 11 |